scispace - formally typeset
Search or ask a question

Showing papers in "Journal of Physics C: Solid State Physics in 1979"


Journal ArticleDOI
TL;DR: In this paper, a dipole moment in the repeat unit perpendicular to the surface in an ionic crystal is demonstrated and the surfaces of any ionic or partly ionic material are classified into three types.
Abstract: When there is a dipole moment in the repeat unit perpendicular to the surface in an ionic crystal, lattice sums in the electrostatic energy diverge and the calculated surface energy is infinite. The cause of this divergence is demonstrated and the surfaces of any ionic or partly ionic material are classified into three types. Type 1 is neutral with equal numbers of anions and cations on each plane and type 2 is charged but there is no dipole moment perpendicular to the surface because of the symmetrical stacking sequence. Both these surfaces should have modest surface energies and may be stable with only limited relaxations of the ions in the surface region. The type 3 surface is charged and has a dipole moment in the repeat unit perpendicular to the surface. This surface can only be stabilised by substantial reconstruction. These conclusions are important for the analysis of the surface structure of ionic crystals.

1,563 citations


Journal ArticleDOI
TL;DR: In this paper, a momentum-space formalism for calculating the total energy of solids is derived, which is designed particularly for application with the self-consistent pseudo-potential method.
Abstract: A momentum-space formalism for calculating the total energy of solids is derived. This formalism is designed particularly for application with the self-consistent pseudo- potential method. In the present formalism, the total energy is obtained through band- structure calculations without involving additional integrations. The Hellman-Feynman theorem is derived, as is a modified virial relation for the pseiidopotential Hamiltonian which provides an alternative way of calculating forces and total energies. The calculation of the total energy of solids and related derivatives with respect to structural degrees of freedom has been an ongoing problem since the early days of solid state physics (Wigner and Seitz 1933, 1934, Fuchs 1935). Quantum-mechanical calcu- lations on molecules suggest that correlation effects might sometimes be responsible for most of their binding energy (Schaefer 1972). The solid state approaches have concentrated on efforts to include most of these effects through an effective potential I/corr(p(r, Y')) (Hohenberg and Kohn 1964, Kohn and Sham 1965), rather than by complicated wave- function-related configuration interactions or many-electron perturbation techniques. Besides the problem of considering correlation effects, the self-consistent solution of the Schrodinger equation within a desired accuracy is quite difficult ; typically, the experi- mental binding energy of elemental solids is 10-4-10-5 times the total energy. These difficulties have inspired a large set of total-energy calculations that circumvents the complete solution of the Schrodinger equation (Harrison 1966, Heine and Weaire 1970). It is based on various approximations to the nearly-free-electron representation and may include the effect of more localised electrons (e.g. d states in transition metals) through specific interaction models (Moriarty 1974, 1977). As the variational self-consistent charge density remains unspecified in this approach, various forms of linear dielectric screening of the basic Coulomb interactions are introduced (Harrison 1966, Heine and Weaire 1970). Another set oftotal-energy calculations is based on direct solutions ofthe Schrodinger equation within a given interaction model : for example, Hartree-Fock (Harris and Monkhorst 1971, Wepfer et al 1974), density-functional (Ching and Callaway 1974,

786 citations


Book ChapterDOI
Glen A. Slack1
TL;DR: In this article, the authors studied the thermal conductivity of non-metallic crystals at temperatures comparable to or higher than the Debye temperature, where the dominant carriers of thermal energy are phonons and the dominant scattering mechanism is the intrinsic phonon-phonon scattering.
Abstract: Publisher Summary This chapter reviews the thermal conductivity of nonmetallic crystals at temperatures comparable to or higher than the Debye temperature. It deals with the intrinsic behavior of such pure crystals at high temperatures. In such crystals, the dominant carriers of thermal energy are phonons and the dominant scattering mechanism to be considered is the intrinsic phonon–phonon scattering. This is a small section of the much larger problem of the thermal conductivity of nonmetallic solids and clearly it neglects possible heat transport by photons, charge carriers, polarons, and magnons. It also neglects other possible phonon scattering mechanisms such as isotopes, impurities, vacancies, charge carriers, dislocations, grain boundaries, and crystal boundaries. It presents the absolute value of the thermal conductivity, K, as determined by phonon–phonon scattering, the temperature dependence of K, the volume dependence of K, the change in K upon melting, and the minimum value of K. The chapter discusses a composite curve for the thermal conductivity versus temperature of pure KCl measured at a constant pressure of, say, one atmosphere.

734 citations


Journal ArticleDOI
TL;DR: In this article, a new percolation problem is posed which can exhibit a first-order transition, where sites on an empty lattice are first randomly occupied, and then all occupied sites with less than a given number m of occupied neighbours are successively removed until a stable configuration is reached.
Abstract: A new percolation problem is posed which can exhibit a first-order transition. In bootstrap percolation, sites on an empty lattice are first randomly occupied, and then all occupied sites with less than a given number m of occupied neighbours are successively removed until a stable configuration is reached. On any lattice for sufficiently large m, the ensuing clusters can only be infinite. On a Bethe lattice for m>or=3, the fraction of the lattice occupied by infinite clusters discontinuously jumps from zero at the percolation threshold. From an analysis of stable and metastable ground states of the dilute Blume-Capel model (1966), it is concluded that effects like bootstrap percolation may occur in some real magnets.

542 citations


Journal ArticleDOI
TL;DR: In this article, a new type of effective field theory of the Ising model is presented and the differential operator method is introduced into the exact spin correlation function identity obtained by Callen.
Abstract: A new type of effective-field theory of the Ising model is presented. The differential-operator method is introduced into the exact spin correlation function identity obtained by Callen. The Curie temperatures are evaluated by using two different types of effective Hamiltonians. It is also shown how the Zernike and the Bethe-Peierls equations can be reproduced within one framework depending on the choice of effective fields in an effective Hamiltonian. The spin correlation function and the specific heat are presented.

529 citations


Journal ArticleDOI
TL;DR: In this paper, a relativistic generalisation of the Hohenberg-Kohn-Sham density functional formalism is presented, in which the many-body effects are included in the formalism via energy functionals analogous to the exchange-correlation functionals of the non-relativistic formalism.
Abstract: A relativistic generalisation of the Hohenberg-Kohn-Sham density functional formalism is presented. Single-particle equations, analogous to those suggested for the non-relativistic formalism are introduced. These equations may take two forms, one analogous to the Dirac-Slater and the other analogous to Dirac-Fock relativistic self-consistent field equations. The complicated relativistic many-body effects are included in the formalism via energy functionals analogous to the exchange-correlation functionals of the non-relativistic formalism. The local density approximation for these functionals is discussed and explicit expressions are given for relativistic corrections. The relation of these corrections to the Breit interaction is mentioned. The description of magnetic effects in the relativistic formalism is discussed briefly.

407 citations


Journal ArticleDOI
TL;DR: In this article, a uniform magnetic field is shown to generate random local fields in uniaxially anisotropic antiferromagnets with random exchange interactions, which leads to a stronger divergence of the temperature derivative of the static susceptibility even at zero field, and to a drastic change in the critical exponents at the Ising-like Antiferromagnetic transition as well as at the tricritical or bicritical points occurring at finite fields.
Abstract: A uniform magnetic field is shown to generate random local fields in uniaxially anisotropic antiferromagnets with random exchange interactions. This leads to a stronger divergence of the temperature derivative of the static susceptibility even at zero field, and to a drastic change in the critical exponents at the Ising-like antiferromagnetic transition as well as at the tricritical or bicritical points occurring at finite fields.

344 citations


Journal ArticleDOI
TL;DR: By extrapolating to 0 and 30 eV experimental data in the energy range from approximately 1-1.3 to 14 eV, a Kramers-Kronig analysis of the reflectivity spectrum at room temperature from the basal plane (E perpendicular to c) of single crystals of 2H-MoS2, 2HMoSe2 and 2H -MoTe2 has been performed.
Abstract: By extrapolating to 0 and 30 eV experimental data in the energy range from approximately 1-1.3 to 14 eV a Kramers-Kronig analysis of the reflectivity spectrum at room temperature from the basal plane (E perpendicular to c) of single crystals of 2H-MoS2, 2H-MoSe2 and 2H-MoTe2 has been performed. The optical data so obtained have been discussed and interpreted in terms of the proposed band model for these materials.

342 citations


Book ChapterDOI
TL;DR: In this article, a review of theoretical models applicable to concentrated solid solutions is presented, focusing on concentrated solutions because dilute ones can be considered as special cases and because the interesting effects of clustering and ordering are most apparent at high solute concentrations.
Abstract: Publisher Summary This chapter reviews current theoretical models applicable to concentrated solid solutions. It focuses on concentrated solutions because dilute ones can be considered as special cases and because the interesting effects of clustering and ordering are most apparent at high solute concentrations. The extended ranges of solubility are often found in metallic systems, and for this reason most examples selected will refer to metals and alloys, although the models presented are equally applied to off-stoichiometric compounds, metallic or inorganic, and to amorphous solids. The chapter provides description of the state of the order of the system through suitable averaging procedures. It discusses the internal energy of solutions, from both electronic and elastic standpoints. The chapter presents free energy models, such as generalized Bragg- Williams's model, Landau theory, and cluster variation method. These models are applied to the study of phase equilibrium.

308 citations


Journal ArticleDOI
TL;DR: In this article, the authors used renormalization theory to calculate the statistical properties of systems with arbitrary finite size, where the system is renormalized until the unit length is of the order of the total length of the original system.
Abstract: Renormalisation theory can be used to calculate the statistical properties of systems with arbitrary finite size. This method is demonstrated with the order parameter is and specific heat for epitaxial ordering. The system is renormalised until the unit length is of the order of the total length of the original system. Then, the renormalised partition function is directly evaluated with an appropriate distribution of boundary conditions. Resulting curves of the rounded transition are compared with experimental data. Underlying the finite-size calculation, Migdal-Kadanoff-type recursion relations for q-state Potts models are adjusted by varying q to yield the expected specific-heat exponent in the infinite-system limit. Additionally, it is noted that, with no adjustment, these recursion relations are self-consistently correct for q to infinity on the triangular lattice, and give the first-order transition at the exact temperature and with probably the exact latent heat.

280 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the density of an eigenstate and its density can be used as the basic variable for calculating the properties of excited states and an extension of the Hohenberg-Kohn-Sham theory for excited states has also been developed.
Abstract: It is shown that the density can be used as the basic variable for calculating the properties of excited states. The correspondence is not between an eigenstate and its density, as is the case with the ground state, but between the subspace spanned by the number of lowest-energy eigenstates and the sum of their densities. An extension of the Hohenberg-Kohn-Sham theory (1964-5) for excited states has also been developed. The equations derived are similar in form to those for the ground-state density but the interpretation is different. The lowest-order approximation of the present theory coincides with Slater's 'transition-state' theory (1974).

Journal ArticleDOI
TL;DR: In this article, a tight-binding method with scaled two-centre interactions was used to calculate the energy and nature of the upper valence bands of SnO2 and the calculated joint density of states for the experimentally observed optical dispersion.
Abstract: The band structures and densities of states for a number of non-transition-metal compounds with the rutile structure are calculated using a tight-binding method with scaled two-centre interactions. For SnO2, the valence band maximum state is calculated to have Gamma 3+ symmetry in agreement with experimental results, and the calculated valence-band density of states is in fair agreement with photoemission. The simplicity of the LCAO approach is utilised to give algebraic expressions for the energy and nature of each band and used to discuss bonding and ionicity. The importance of the long-pair oxygen orbitals in forming the upper valence bands of SnO2 is stressed. TeO2 is discussed as an example of a class of compounds in which the two cation s electrons remain bound, giving rise to a cationic gap. The calculated joint density of states can be used to account for the experimentally observed optical dispersion.

Journal ArticleDOI
TL;DR: The power law which characterises the behaviour of the conductivity of an inhomogeneous conductor near the percolation threshold should generally be independent of the distribution from which the conducting elements are chosen.
Abstract: The power law which characterises the behaviour of the conductivity of an inhomogeneous conductor near the percolation threshold should generally be independent of the distribution from which the conducting elements are chosen. Some counterexamples, in which a sufficiently anomalous distribution can alter the conduction threshold exponents, are exhibited. Specifically, it is claimed that a network randomly composed of insulating bonds ( sigma =0) and bonds chosen from a distribution behaving as sigma - alpha for small sigma will give the usual exponent t for alpha 2, but in the case 1< beta

Journal ArticleDOI
TL;DR: The reflectivity of magnetite (Fe3O4) has been measured in the spectral energy range between 003 and 12 eV by means of a Kramers-Kronig analysis.
Abstract: The reflectivity of magnetite (Fe3O4) has been measured in the spectral energy range between 003 and 12 eV The optical constants have been determined by means of a Kramers-Kronig analysis The interband transition spectrum can be interpreted by O 2p to Fe4s transitions and be Fe3dn to 3dn-14s orbital promotion processes including final-state effects of the atom-like 3dn-1 configurations

Journal ArticleDOI
TL;DR: In this paper, a theory for the memory function of the velocity autocorrelation function for a monatomic liquid is presented, based on a general kinetic approach, and strong emphasis is put on the coupling of the motion of a single particle to the collective motions in its surrounding.
Abstract: A theory for the memory function of the velocity autocorrelation function for a monatomic liquid is presented, based on a general kinetic approach. Strong emphasis is put on the coupling of the motion of a single particle to the collective motions in its surrounding, splitting the memory function into an essentially binary collision part and a more collective tail, including recollisions to all orders. Numerical comparisons with molecular dynamics data on liquid rubidium have shown quite remarkable agreement.

Journal ArticleDOI
TL;DR: In this article, the dielectric constant epsilon e or the conductivity sigma e of a two-phase composite is calculated for a simple cubic array of identical spherical inclusions embedded in a homogeneous host.
Abstract: New methods are described for calculating the dielectric constant epsilon e or the conductivity sigma e of a two-phase composite and these are applied to a simple cubic array of identical spherical inclusions embedded in a homogeneous host. A spectral representation is derived for epsilon e, and numerical results are presented for the poles and the residues. Analytical and numerical methods are used to discuss the conductivity threshold of the cubic array, which occurs when the host is an insulator and the conducting spheres begin to touch each other. It is argued that sigma e as a function of sigma 1/ sigma 2 has an essential singularity at the conductivity threshold.

Journal ArticleDOI
TL;DR: In this paper, a modified form of the electron-gas approximation is proposed for the calculation of interionic potentials in the solid state, and the results of these potentials are calculated and compared both with experiment and with the results derived from other theoretical methods.
Abstract: For pt.I see ibid., vol.10, no.9, p.1431 (May 1977). A modified form of the electron-gas approximation is proposed for the calculation of interionic potentials in the solid state. On the basis of these potentials perfect lattice and defect properties of a number of solids are calculated and compared both with experiment and with the results derived from other theoretical methods. The cohesive energies, lattice constants and compressibilities of a wide range of oxides are considered, while the defect energies for NaCl, MgO, MnO, CaF2 and MgF2 are examined in detail. From the results presented it is concluded that for solids such as the alkali and alkaline-earth halides and the alkaline-earth oxides, which are largely ionic, the modified electron-gas approximation is a reliable non-empirical method for the calculation of interionic potentials.

Journal ArticleDOI
TL;DR: In this paper, a resolution to the order k6 of the three-level equation of Kane allows the authors to obtain a new expression for the conduction band energy and so new analytical expressions for the electron effective masses in the range of carrier concentration 1016-1019 cm-3.
Abstract: A resolution to the order k6 of the three-level equation of Kane allows the authors to obtain a new expression for the conduction band energy and so new analytical expressions for the electron effective masses in the range of carrier concentration 1016-1019 cm-3. The calculated values of the conduction effective mass as a function of carrier density agree well, for the first time, with experimental values, which were obtained from Shubnikov-de Haas experiments by using a new expression for the oscillation amplitude. In this expression the authors take into account the effect of medium-range potential fluctuations induced by crystal inhomogeneities.

Journal ArticleDOI
TL;DR: In this article, the structural phase transitions occurring in PbZrO3 have been investigated using X-ray diffraction and dielectric constant measurements, and the lattice parameters, Pb ion displacements and ZrO6 octahedral tilts in the antiferroelectric, orthorhombic phase have been determined as functions of temperature between 20 and 228 degrees C using continuously recording X-Ray diffraction photography.
Abstract: The structural phase transitions occurring in PbZrO3 have been investigated using X-ray diffraction and dielectric constant measurements. The lattice parameters, Pb ion displacements and ZrO6 octahedral tilts in the antiferroelectric, orthorhombic phase have been determined as functions of temperature between 20 and 228 degrees C using continuously recording X-ray diffraction photography. The temperature dependence of the Pb ion displacement is discussed with reference to the Kittel theory of antiferroelectricity. The lattice parameters and structural data derived from these results are used to describe the temperature dependence of the birefringence in PbZrO3.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the time dependence of delayed radiation when a pulse of synchrotron radiation undergoes resonance Bragg scattering by the nuclei in a crystal that have an isomeric level with a Mossbauer transition.
Abstract: The time dependence of delayed radiation is investigated when a pulse of synchrotron radiation undergoes resonance Bragg scattering by the nuclei in a crystal that have an isomeric level with a Mossbauer transition. Instead of the usual exponential law exp(-t/ tau 0) characteristic of an isolated nucleus, a time dependence in the form ( tau 0/t)2 exp(-t/ tau 0) was discovered at small deviations alpha from the Bragg angle. The acceleration of the decay is connected with the collective nature of the excitation of the nuclei in the crystal-the nuclear exciton formation. The exponential law remains at large alpha but the intensity decreases as 1/ alpha 2. In the case of large divergence of the incident beam the law ( tau 0/t) exp(-t/ tau 0) is obeyed. The frequency distribution of the reflected pulse and the possibility of formation of a resonance structure with sufficient resolution are analysed in detail.

Journal ArticleDOI
TL;DR: In this article, the mean field equations for the long-range spin-glass model were solved numerically for T
Abstract: Mean-field equations for the long-range spin-glass model are solved numerically for T

Journal ArticleDOI
G Davies1
TL;DR: In this paper, two commonly occurring radiation damage centres in diamond were measured and their zero-phonon lines were shown to be electric-dipole transitions between E (ground) and A1, or A2, (excited) states at trigonal centres (C3, C3v of D3d).
Abstract: Uniaxial stress measurements are reported on two commonly occurring radiation damage centres in diamond. Their zero-phonon lines, at 17380 and 23530 cm-1; are shown to be electric-dipole transitions between E (ground) and A1, or A2, (excited) states at trigonal centres (C3, C3v of D3d). Other non-degenerate states are found approximately 100 cm-1 above the ground level. The data are consistent with dynamic Jahn-Teller distortions occurring in the ground states of the centres. On bringing together information on all the known degenerate electronic states at trigonal centres in diamond, two simple generalisations emerge for the occurrence of Jahn-Teller effects at these centres.

Journal ArticleDOI
TL;DR: In this article, generalisations of the rational eigenvalues found by Thorson and Moffitt for the Jahn-Teller system Gamma 8(X) tau 2 are studied.
Abstract: Generalisations of the two apparently rational eigenvalues found by Thorson and Moffitt for the Jahn-Teller system Gamma 8(X) tau 2 are studied. Equations of finite order are established for determining the strength D of the Jahn-Teller interaction of which an eigenvalue lies on a baseline. (A baseline is the line that constitutes the asymptote of a sequence of rotational levels that come into existence as D tends to infinity.) The analysis is extended to the system E(X) epsilon and is illustrated by a number of special examples.

Journal ArticleDOI
TL;DR: In this article, the structural distortions and changes in electronic structure around the Fermi level produced by the CDW-PLD state were investigated for layered dichalcogenides, the linear chain platinum complex KCP, and the organic charge transfer salts.
Abstract: At low temperatures, low dimensional metals are commonly found to exhibit superlattices incommensurate with the primitive lattice (periodic lattice distortion coupled to charge density waves, PLD — CDW). Transitions to such states are driven by strong electron phonon coupling and favoured by the particular forms of the Fermi surfaces of these metals. Experimental investigations of the structural distortions, and of the changes in electronic structure around the Fermi level produced by the CDW — PLD state, will be discussed for the layered dichalcogenides, the linear chain platinum complex KCP, and the organic charge transfer salts.

Journal ArticleDOI
TL;DR: In this article, the density of states (DS) of a disordered system with localised electronic states is studied in the vicinity of the Fermi level with the Monte-Carlo computer simulation for the two-and three-dimensional simple model.
Abstract: The density of states (DS) of a disordered system with localised electronic states is studied in the vicinity of the Fermi level with the Monte-Carlo computer simulation for the two- and three-dimensional simple model. The minimisation of the total energy with respect to all one-electron transitions is shown to be a good approximation both for the total energy and for the DS. The electron-electron interaction drastically changes the DS in the vicinity of the Fermi level. The DS is shown to have a 'soft' Coulomb gap, and the self-consistent equation fits the results of simulation well. The finite size effect is also studied.

Journal ArticleDOI
TL;DR: In this article, two extensions of the widely used tetrahedron method for the evaluation of spectral properties of solids are presented, including matrix element variation inside tetrahedral microzones in the same spirit in which the energy variation is included in the original method.
Abstract: Two extensions of the widely used tetrahedron method for the evaluation of spectral properties of solids are presented. The first provides explicit formulae for including matrix element variation inside tetrahedral microzones in the same spirit in which the energy variation is included in the original method. The second is a scheme for using local quadratic interpolation inside some tetrahedra to provide the matrix element and energy values required to apply the tetrahedron method to a large number of tetrahedra into which the original tetrahedra have been divided. This scheme is similar to the hybrid method of extension of the Gilat-Raubenheimer method. Application to the calculation of the density of states of a single tight-binding band in a FCC crystal shows that its efficiency is comparable with that of the method recently proposed by Chen (1977).

Journal ArticleDOI
TL;DR: In this article, the results of a neutron diffraction study on the short-range order in the TeO2-Li2O glassy system were presented, and a model for structural recombination in TeO4 tetrahedra for tellurite glasses was proposed.
Abstract: The results of a neutron diffraction study on the short-range order in the TeO2-Li2O glassy system are presented. On the basis of the obtained atomic radial distribution function a model for structural recombination in TeO4 tetrahedra for tellurite glasses is proposed. This model takes into account the influence of the modifier and the free-electron pair of the Te atom in TeO4 polyhedra. The limits of applicability to this system of the modified structural diffusion model and the model proposed are established.

Journal ArticleDOI
TL;DR: In this article, the band structures of the layer compounds SnS2, SnSe2, CdI2 and PbI2 are calculated by the tight-binding method, and a universal band structure for the family is found by use of approximate algebraic band energies.
Abstract: The band structures of the layer compounds SnS2, SnSe2, CdI2 and PbI2 are calculated by the tight-binding method. They are in closer agreement with experimental results and previous pseudopotential calculations than previous tight-binding results have been. A universal band structure for the family is found by use of approximate algebraic band energies. For the 16-electron crystals a Gamma 2- to L1+ indirect gap and a main optical transition due to anion p-cation p orbitals is found, whilst for PbI2 the gap is direct at A.

Journal ArticleDOI
TL;DR: The n-to-0 replica method is used to study the Ising spin glass below its transition temperature in this paper, where the order parameter correlation functions are shown to contain massless modes ('replicon' modes) within mean-field theory.
Abstract: The n to 0 replica method is used to study the Ising spin glass below its transition temperature. The order parameter correlation functions are shown to contain massless modes ('replicon' modes) within mean-field theory. These become unstable at first order in perturbation theory about the mean-field solution. An alternative formulation of perturbation theory, however, yields a family of new solutions which break, in general, the symmetry between the replicas. Stability requirements single out a unique member of this family which exhibits (i) massless moded, and (ii) a restoration of replica symmetry. Within the framework of the new solution, perturbation theory for the order parameter (Qalpha beta ) breaks down for dimensionalities d

Journal ArticleDOI
TL;DR: In this paper, a model for magnetic ordering around the defect clusters was proposed based on Catlow and Fender's model, showing that the number of spins lying in the (111) plane is consistent with Catlow's model.
Abstract: Neutron diffraction experiments have been carried out at room temperature and 42K on polycrystalline samples of FezO with z=0943, 0938 and 0929 At room temperature, the ratio of octahedral iron vacancies to tetrahedral iron interstitials is close to 3 and is therefore in agreement with the defect cluster proposed by Catlow and Fender (1975) Examination of the 42K data has led to a model for magnetic ordering around the clusters The interstitial cations and surrounding iron atoms are coupled by an antiferromagnetic exchange interaction The spins in this region lie in the (111) plane, not along (111) as in the defect-free regions The number of spins lying in the (111) plane is consistent with Catlow and Fender's model